A food stand at baseball gam e sells food & drinks. Manager sampled 100 customer

Question

A food stand at baseball game sells food & drinks. Manager sampled 100 customers about their hotdog and got the following result.

Then the manager of the food concession adds info on beer sales. In particular, he determines that the joint probability of hotdogs & beer purchases are as follows:

Purchase Beer:                               

                                   Yes        No                                         

Buy               Yes         0.4          0.1                               

HotDog:         No          0.2          0.3                          

QUESTIONs:

a. Are the above probabilities consistent with the data in problem #4? Explain your answer.

b. Determine the probability that a customer purchases beer, given that he has purchased a hotdog.

c. Are the probabilities of beer and hot dog purchase independent? Explain your answer.

Explanation / Answer

a) Yes as probability of buying hot dog =50/100 =0.5

and not buying =1-0.5 =0.5

b)  probability that a customer purchases beer given purcahsed hot dog =0.4/0.5 =0.8

c) asP( purchases beer) =0.4+0.2 =0.6 which is not equal to probability that a customer purchases beer given purcahsed hot dog ; therefore probabilities of beer and hot dog purchase are not independent.

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